a person invests some money in a 4% stock at a 10% discount.he gained rs 300 on selling the stock when it was quoting at a 10% premium.this money was invested in a 3% stock t rs75 and sold at a price of rs80 per stock.how much profit/loss did he make over his initial investment? (a) rs 305 profit (b) rs 320 loss (c) rs 410 profit (d) rs 480 loss

Let's break down the problem step by step.

### Step 1: Initial Investment in 4% Stock
- The person invests in a **4% stock at a 10% discount**.
- Let the **face value** of the stock be \( F \).

Since it's at a **10% discount**, the **purchase price** of the stock would be:
\[
\text{Purchase Price} = F \times \left(1 - \frac{10}{100}\right) = 0.9F
\]

The annual dividend (income) from a **4% stock** on the face value is:
\[
\text{Annual Dividend} = 4\% \text{ of } F = \frac{4}{100} \times F = 0.04F
\]

### Step 2: Selling the Stock
- The person **gains Rs 300** by selling the stock when it is at a **10% premium**.
- The **selling price** of the stock at a 10% premium is:
\[
\text{Selling Price} = F \times \left(1 + \frac{10}{100}\right) = 1.1F
\]

The gain is given by:
\[
\text{Gain} = \text{Selling Price} - \text{Purchase Price}
\]
We know the gain is Rs 300, so:
\[
1.1F - 0.9F = 300
\]
\[
0.2F = 300
\]
\[
F = \frac{300}{0.2} = 1500
\]

Now, we know the **face value** \( F = 1500 \).

- The **purchase price** of the stock was \( 0.9 \times 1500 = 1350 \).
- The **selling price** of the stock was \( 1.1 \times 1500 = 1650 \).

Thus, the **person sells the stock for Rs 1650** after buying it for Rs 1350, gaining Rs 300.

### Step 3: Reinvesting in 3% Stock
- The person now has Rs 1650 (from selling the first stock) and invests it in a **3% stock at Rs 75 per stock**.

The number of stocks bought:
\[
\text{Number of Stocks} = \frac{1650}{75} = 22
\]

### Step 4: Selling the 3% Stock
- The person sells the **3% stock at Rs 80 per stock**.
- The total selling price is:
\[
\text{Total Selling Price} = 22 \times 80 = 1760
\]

### Step 5: Profit or Loss Calculation
The initial investment was Rs 1350 (in the 4% stock), and the final amount after selling the second stock is Rs 1760.

Thus, the profit is:
\[
\text{Profit} = 1760 - 1350 = 410
\]

So, the person made a **profit of Rs 410**.

### Final Answer:
The correct option is:
\[
\boxed{\text{(c) Rs 410 profit}}
\]

---

Would you like any more details or further clarification?

Here are 5 related questions for practice:
1. If the stock was sold at a 15% premium, what would the profit be?
2. What would be the loss if the person sold the 3% stock at Rs 70 per stock?
3. How much would the person have gained if the initial investment was in a 5% stock?
4. What is the profit percentage over the initial investment?
5. How many stocks could the person buy if the second stock price was Rs 90?

**Tip:** Always break down investment problems into smaller steps involving price, premium/discount, and dividend to avoid confusion.

A person invests some money in a 4% stock at a 10% discount. He gained Rs 300 on selling the stock when it was quoting at a 10% premium. This money was invested in a 3% stock at Rs 75 and sold at a price of Rs 80 per stock. How much profit/loss did he make over his initial investment? (a) Rs 305 profit (b) Rs 320 loss (c) Rs 410 profit (d) Rs 480 loss

Learn how to calculate the profit made from investing in a 4% stock at a 10% discount and selling at a 10% premium. This problem involves concepts like stock prices, percentage profit, and reinvestment into another stock at Rs 75 per share. A step-by-step guide to solving for a Rs 410 profit. Suitable for students in Grades 9-11.

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